polynomial and interval arithmetic

I would like to evaluate a polynomial on a real interval (an element of RIF). My problem is the following. I take the polynomial x(1-x) which is increasing on (0,1/2). Hence, if I have an interval (l,u) in (0,1/2) and I apply this polynomial, I would like to get an answer close to (l(1-l), u(1-u)) up to rounding error. But what I get is (l(1-u), u(1-l)) which is twice bigger! The following code illustrates the behavior:

1 answer

Quadratic polynomials like yours can be rephrased as Single Use Expressions by
completing the square. General polynomials not so easy unless you can factor.
Use google to search for terms in this answer that might not be familiar.
Richard Fateman